We open by remembering yesterday's imaginary river adventure. I have students retell one or two of the mini-stories about what one of the children brought on their river adventure, emphasizing the multiplication fact but also using the addition model for multiplication and making certain that students can express these problems, with assistance, as both repeated addition and multiplication.

We write up the patterns for counting by 3, 4, 6, 7, 9 and chorally count. I invite students to explain any patterns they see but leave it open ended - if a pattern is accurate but not one that helps learn the facts, ask them how that might help them. Who knows, maybe they will think of something the teacher has not!

Model writing an equation, a model, and a story sentence for 10 x 3 and 10 x 4. Either use the template from yesterday, with the tubes already on it, or draw your own. Simple doughnut rings suffice.

Next, we brainstorm a list of 10 different objects that could be used in a tubing story. It is important to have a list generated by the students, so if any child later can't think of an object for their story, they have somewhere to refer to. This also supports ELL students.

In real life, on a tubing adventure, one takes the bare minimum number of items. If your students are from a place with rivers, they may be aware of this. Tell them you are counting up all the items each child takes on this adventure, so that they will return it all after their river adventure is over!

At the end of this activity, I expect students to be able to use a drawing they create to tell a one sentence story to represent all of the following facts:

10 x 1

10 x 2

10 x 3

10 x 4

10 x 5

10 x 6

10 x 7

10 x 8

10 x 9

They also are expected to arrive at the solution for each of the equations by both flipping the problem and by skip counting using their pictures.

Of course, for the long term it is in no way desirable for students to arrive at the answer 80 by adding 8 + 8 + 8 + 8 + 8 + 8 + 8 = 8 + 8 + 8 = but for the purpose of this beginning of the year lesson, it is a valid approach because the emphasis is on understanding.

It is a great way to help them to see that multiplication is a faster way to do repeated addition, it shows them that they can use a model they know (addition) to arrive at the product of a multiplication equation, and it may begin to convince them that learning their math facts is far preferable (easier and faster) than constantly building models or adding on to find large products!

In this activity there is a heavy emphasis on Mathematical Practice 1 - make sense of problems and persevere in solving them and Mathematical Practice 6 - attend to precision by demonstrating that counting on with the factor other than ten leads to the same answer.

Place the students into partnerships, preferably using a list so that they are not always w/a seat neighbor or a friend of their choosing. Ask them to share one of their math stories with their partner. Then call on 3 students to share out to the class a multiplication story, with an equation with a factor of 10, that their partner created. Ask them what they think of using repeated addition to solve multiplication problems with a large factor (7, 8, 9). It is NOT wrong if they say they like it, nor is it right if they say multiplication is better. Keep teacher opinion out of it and encourage them to think out loud using mathematical terms and compete sentences.

If they have not finished their drawing, their story, or their key, it can go home as homework or perhaps in a structured after-school activity the student will receive support in getting their homework completed.

To encourage them to apply the drawing repeated addition model in a meaningful way, I give them two nights to complete it. That way it was a neat resource that they could use later on in the year.

Another HW or extension option (my students did this as morning work) is to have the students write 3-4 multiplication stories with factors of ten that are independent of the tubing scenario.

Big Idea:
After partners have worked with each other and have some practice creating arrays, it is time to challenge them to define the concept demonstrated by an array and how it can be used to solve problems.